The orthogonal coefficients (REF ) turn out to express [1]} as
\(\mathcal {I}^{\mathbf {\omega }}_{\mathbf {a}}=\sum _{\sigma \in \mathcal {P}_{2q}}\sum _{\tau \in \mathcal {P}_{2q}}\: \delta _{\sigma }({\mathbf {\omega }})\: \delta _{\tau }({\mathbf {a}})\: \mbox{Wg}(\ell (\sigma \vee \tau ))\) 
